Loose Legendrian embeddings in high dimensional contact manifolds

2012/01/11 by Emmy Murphy, Murphy, Emmy · 6 citations
Mathematics · #53D10 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1201.2245

openalex publication_date 2012/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an h--principle type result for a class of Legendrian embeddings in contact manifolds of dimension at least 5. These Legendrians, referred to as loose, have trivial pseudo-holomorphic invariants. We demonstrate they are classified up to Legendrian isotopy by their smooth isotopy class equipped with an almost complex framing. This result is inherently high dimensional: analogous results in dimension 3 are false.

Cited by

• C⁰-rigidity of Legendrians and coisotropics via sheaf quantization
• On positive loops of loose Legendrian embeddings
• Flexible Weinstein manifolds
• Convex Integration Theory without Integration
• The topology of rationally and polynomially convex domains
• Legendrian doubles, twist spuns, and clusters

Related

• h-principle for loose Legendrian embeddings
• On positive loops of loose Legendrian embeddings
• Legendrian Submanifolds in R²ⁿ⁺¹ and Contact Homology
• Constructions and Isotopies of High-Dimensional Legendrian Spheres
• Legendrian Contact Homology in P X R